(1+x^(2))y'+2xy=4x^(2),y(0)=0

(1+x^(2)) dy/dx + 2xy = 4x^(2), given y = 0 , when x = 0

Solve each of the following initial value problems: (dy)/(dx)+(2x)/(x^(2)+1)y=(1)/((x^(2)+1)^(2)),y(0)=0( ii) (x^(2)+1)y'-2xy=(x^(4)+2x^(2)+1)cos x,y(0)=0

The number of triangles formed by the lines represented by x^(3)-x^(2)-x-2=0 and xy^(2)+2xy+4x-2y^(2)-4y-8=0 are

Solve: (1+x^(2))(dy)/(dx)+2xy-4x^(2)=0 subject to the initial condition y(0)=0

If x=sin((1)/(a)log y), show that (1-x^(2))y_(2)-xy_(1)-a^(2)y=0

If x=sin((1)/(a)log y), show that (1-x^(2))y_(2)-xy_(1)-a^(2)y=0

Let y'=(4y^(2)+4xy+x^(2))/(4x^(2)) and y(1)=0 then y(e^((pi)/(2))) equals

Solve : (1+x^(2)+y^(2)+x^(2)y^(2))dx+xy dy=0 , given that y=0 when x=1 .